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systems analysis and design using matlab

Questions and Answers of Systems Analysis And Design Using MATLAB

30.Measurements of the concentration, C, of a substance during a chemical reaction at different times t are shown in the table.(a) Suppose that the data can be modeled with an equation in the
29. Estimated values of thermal conductivity of silicon at different temperatures are given in the following table.(a) Make a plot of k versus T using log scale on both axes.(b) Curve-fit the data
28. Write a user-defined function that determines the best fit of an exponential function of the form . Name the function [b,m] =expofit(x,y), where the input arguments x and y are vectors with the
27. The standard air density, D (average of measurements made), at different heights, h, from sea level up to a height of 33 km is given below.(a) Make the following four plots of the data points
26. The following points are given:(a) Fit the data with a first-order polynomial. Make a plot of the points and the polynomial.(b) Fit the data with a second-order polynomial. Make a plot of the
25. Use the growth data from Problem 24 for the following:(a) Curve-fit the data with a third-order polynomial. Use the polynomial to estimate the height in day 40.(b) Fit the data with linear and
24. Growth data of a sunflower plant is given in the following table:x –5 –4 –1 1 4 6 9 10 y 12 10 6 2 –3 –6 –11 –12 h (ft) –1,000 0 3,000 8,000 15,000 22,000 28,000 T ( °F ) 213.9
23. The number of bacteria measured at different times t is given in the following table. Determine an exponential function in the form that best fits the data. Use the equation to estimate the
22. The U.S. population in selected years between 1815 and 1965 is listed in the table below. Determine a quadratic equation in the form, where t is the number of years after 1800 and P is the
21. The boiling temperature of water at various altitudes h is given in the following table. Determine a linear equation in the form that best fits the data. Use the equation for calculating the
20. The following data is given:(a) Use linear least-squares regression to determine the coefficients m and b in the function that best fits the data.(b) Make a plot that shows the function and the
19. Consider the parabola:, and the point.(a) Write a polynomial expression for the distance d from point P to an arbitrary point Q on the parabola.(b) Make a plot of d versus y for.(c) Determine the
18. A cylinder with base radius r and height h is constructed inside a sphere such that it is in contact with the surface of a sphere, as shown in the figure.The radius of the sphere is in.(a) Create
17. Write a user-defined function that calculates the maximum (or minimum) of a quadratic equation of the form:Name the function [x,y,w] = maxormin(a,b,c). The input arguments are the coefficientsa,
16. Write a user-defined function that multiplies two polynomials. Name the function p=polymult(p1,p2). The two input arguments p1 and p2 are vectors of the coefficients of the two polynomials. The
15. Write a user-defined function that adds or subtracts two polynomials of any order. Name the function p=polyadd(p1,p2,operation). The first two input arguments p1 and p2 are the vectors of the
14. The probability P of selecting three distinct numbers out of n numbers is calculated by:Determine how many numbers, n, should be in a lottery game such that the probability of matching three
13. A rectangular box (no top) is welded together using sheet metal. The length of the box’s base is 18 in. longer than its width. The total surface area of the sheet metal that is used is 2,500
12. An aluminum container has the geometry shown in the figure (the bottom part is a rectangular box and the top is half a cylinder). The outside dimensions are shown. The wall thickness of the
11. A rectangular steel container (no top) has the outside dimensions shown in the figure. The thickness of the bottom surface is t, and the thickness of side walls is . Determine t if the weight of
10. The product of three distinct integers is 6,240. The sum of the numbers is 85. The difference between the largest and the smallest is 57. Using MATLAB’s built-in functions for operations with
9. The product of three integers with spacing of 3 between them (e.g., 9, 12, 15)is 11,960. Using MATLAB’s built-in functions for operations with polynomials, determine the three integers.
8. The product of four consecutive even integers is 1,488,384. Using MATLAB’s built-in function for operations with polynomials, determine the two integers.
7. Use MATLAB to divide the polynomial by the polynomial.
6. Use MATLAB to divide the polynomial by the polynomial .
5. Use MATLAB to carry out the following multiplication of polynomials:Plot the polynomial in the domain .
4. Use MATLAB to carry out the following multiplication of two polynomials:
3. Determine the polynomial that has roots at , ,, and . Make a plot of the polynomial in the domain.
2. Plot the polynomial in the domain .First create a vector for x, next use the polyval function to calculate y, and then use the plot function.
1. Plot the polynomial in the domain. First create a vector for x, next use the polyval function to calculate y, and then use the plot function.
40. In lottery the player has to guess correctly r numbers that are drawn out of n numbers. The probability, P, of guessing m numbers out of the r numbers can be calculated by the expression:where .
39. The first derivative of a function at a point can be approximated with the four-point central difference formula:where h is a small number relative to . Write a user-defined function function
38. A circuit that filters out a certain frequency is shown in the figure. In this filter, the ratio of the magnitudes of the voltages is given by:where , and f is the frequency of the input
37. The simple RC high-pass filter shown in the figure passes signals with frequencies higher than a certain cutoff frequency. The ratio of the magnitudes of the voltages is given by:where , and f is
36. The area moment of inertia of a rectangle about the axis passing through its centroid is . The moment of inertia about an axis x that is parallel to is given by , where A is the area of the
35. Write a user-defined function that determines the coordinate of the centroid of the Ishaped cross-sectional area shown in the figure.For the function name and arguments, use yc
34. The Taylor series expansion for about is given by:where x is in radians. Write a user-defined function that determines using Taylor’s series expansion. For function name and arguments, use
33. In a lottery the player has to select several numbers out of a list. Write a user-defined function that generates a list of n integers that are uniformly distributed between the numbers a andb.
32. Delta rosette is a set of three strain gages oriented at 120° relative to each other. The strain measured with each of the strain gages is , , and . The principal strains and can be calculated
31. The shortest distance between two points on the surface of the globe (greatcircle distance) can be calculated by using the haversine formula. If and are the latitude and longitude of point 1 and
30. Write a user-defined MATLAB function that calculates the determinant of a matrix by using the formula:For the function name and arguments, use d3 = det3by3(A), where the input argument A is the
29. Write a user-defined MATLAB function that finds the largest element of a matrix. For the function name and arguments, use [Em,rc] = matrixmax(A), where A is any size matrix. The output argument
28. Write a user-defined function that sorts the elements of a matrix. For the function name and arguments, use B = matrixsort(A), where A is any size matrix and B is a matrix of the same size with
27. Write a user-defined function that sorts the elements of a vector from the largest to the smallest. For the function name and arguments, use y=downsort(x). The input to the function is a vector x
26. Write a user-defined function that determines the value that occurs most often in a set of data that is given in a two-dimensional matrix. For the function name and arguments, use [v, q]
25. Write a user-defined function that determines the polar coordinates of a point from the Cartesian coordinates in a two-dimensional plane. For the function name and arguments, use [th
24. The harmonic mean H of a set of n positive numbers is defined by:Write a user-defined function that calculates the harmonic mean of a set of numbers. For function name and arguments use
23. Write a user-defined function that determines if a number is a prime number.Name the function pr=Trueprime(m), where the input arguments m is a positive integer and the output argument pr is 1 if
22. In polar coordinates a two-dimensional vector is given by its radius and angle . Write a user-defined MATLAB function that adds two vectors that are given in polar coordinates. For the function
21. Write a user-defined function that plots an ellipse with axes that are parallel to the x and y axes, given the coordinates of its vertices and the coordinates of another point that the ellipse
20. Write a user-defined function that plots a triangle and the circle that is inscribed inside, given the coordinates of its vertices. For the function name and arguments, use TriCirc(A,B,C). The
19. Write a user-defined MATLAB function that converts integers written in decimal form to binary form. Name the function b=Bina(d), where the input argument d is the integer to be converted and the
18. Write a user-defined function that determines the location of the center and the radius of a circle that passes through three given points in a plane. The function also creates a plot that shows
17. As shown in the figure, the area of a convex polygon can be calculated by adding the area of the triangles that the polygon can be divided into. Write a userdefined MATLAB function that
16. The area of a triangle ABC can be calculated by:where AB is the vector from vertex A to vertex B and AC is the vector from vertex A to vertex C. Write a user-defined MATLAB function that
15. Write a user-defined MATLAB function that determines the cross product of two vectors. For the function name and arguments, use w=crosspro(u,v). The input arguments to the function are the two
14. Write a user-defined MATLAB function that determines the unit vector in the direction of the line that connects two points (A and B) in space. For the function name and arguments, use n =
13 Write a user-defined MATLAB function that determines the time elapsed between two events during a day. For the function name and arguments, use dt = timediff(TA,ap1,TB,ap2). The input arguments to
12. Write a user-defined MATLAB function that determines the angle that forms by the intersection of two lines. For the function name and arguments, use th=anglines(A,B,C). The input arguments to the
11. Write a user-defined function that calculates grade point average (GPA) on a scale of 0 to 5, where , , , , and . For the function name and arguments, use GPA = GradePtAve(G,C). The input
10. The relative humidity, RH, at sea level can be calculated from measured values of the dry-bulb temperature, , and the wet-bulb temperature by(temperatures in degrees Celsius):where VP is the
9. A paper cup is designed to have a geometry of a frustum of a cone. Write a user-defined function that determines the volume and the surface area (side plus bottom) of the cup for given values of
8. The fuel tank shown in the figure in shaped as a half a sphere with in.Write a user-defined function that calculates the volume of fuel in the tank (in gallons) as a function of the height y
7. The body surface area (BSA) in m2 of a person (used for determining dosage of medications) can be calculated by the formula (Mosteller formula):in which H is the person’s height in inches, and W
6. Write a user-defined MATLAB function that converts torque given in units of N-m to torque in units of lb-ft. For the function name and arguments, use lbft = NmTOlbft(Nm). The input argument Nm is
5. Tables of material properties list density, in units of kg/m3, when the international system of units (SI) is used, and list specific weight, in units of lb/in.3, when the U.S. customary system of
4. Pressure in U.S. customary units is measured in psi (pound per square inch).In SI metric units pressure is measured in Pa (N/m2). Write a user-defined MATLAB function that converts pressure given
3. In the U.S. fuel efficiency of cars is specified in miles per gallon (mpg). In Europe it is often expressed in liters per 100 km. Write a MATLAB userdefined function that converts fuel efficiency
2. Write a user-defined MATLAB function for the following math function:The input to the function is (in radians) and the output is r. Write the function such that can be a vector.(a) Use the
1. Write a user-defined MATLAB function for the following math function:The input to the function is x and the output is y. Write the function such that x can be a vector (use element-by-element
39. The following MATLAB commands create a sine-shaped signal y(t) that contains random noise:t = 0:.05:10;y = sin(t)-0.1+0.2*rand(1,length(t));Write a MATLAB program that uses these commands to
38. A Keith number is a number (integer) that appears in a Fibonacci-like sequence that is based on its own decimal digits. For two-decimal digit numbers(10 through 99) a Fibonacci-like sequence is
37. The overall grade in a course is determined from the grades of 10 homework assignments, 2 midterms, and a final exam, using the following scheme:Homework: Homework assignments are graded on a
36. The roots of a cubic equation can be calculated using the following procedure:Set: , , and .Calculate: , where and .If the equation has complex roots.If all roots are real and at least two are
35. The Sierpinski triangle can be implemented in MATLAB by plotting points iteratively according to one of the following three rules that are selected randomly with equal probability.Rule 1: , Rule
34. In a one-dimensional random walk, the position x of a walker is computed by:where s is a random number. Write a program that calculates the number of steps required for the walker to reach a
33. Write a program in a script file that converts a measure of area given in units of either m2, cm2, in2, ft2, yd2, or acre to the equivalent quantity in different units specified by the user. The
32. One numerical method for calculating the cubic root of a number, is Halley’s method. The solution process starts by choosing a value as a first estimate of the solution. Using this value, a
31. The concentration of a drug in the body can be modeled by the equation:where is the dosage administered (mg), is the volume of distribution(L), is the absorption rate constant (h–1), is the
30. Write a program that determines the change given back to a customer in a self-service checkout machine of a supermarket for purchases of up to $50.The program generates a random number between
29. Write a program in a script file that calculates the cost of renting a car according to the following price schedule:The program asks the user to enter the type of car (sedan or SUV), the number
28. Body mass index (BMI) is a measure of obesity. In standard units, it is calculated by the formula where W is weight in pounds, and H is height in inches. The obesity classification is:Write a
27. The following are formulas for calculating the training heart rate (THR):where MHR is the maximum heart rate given by (https://en.wikipedia.org/wiki/Heart_rate):For males: , for females: , RHR is
26. Write a MATLAB program in a script file that finds a positive integer n such that the sum of all the integers is a number between 100 and 1,000 whose three digits are identical. As output, the
25. The Taylor series expansion for ax is:Write a MATLAB program that determines ax using the Taylor series expansion. The program asks the user to type a value for x. Use a loop for adding the terms
24. A list of exam scores (S) (in percent out of 100%) is given: 72, 81, 44, 68, 90, 53, 80, 75, 74, 65, 50, 92, 85, 69, 41, 73, 70, 86, 61, 65, 79, 94, 69.Write a computer program that calculates
23. A perfect number is a positive integer that is equal to the sum of its positive divisors except the number itself. The first two perfect numbers are 6 and 28 since and . Write a computer program
22. A Mersenne prime is a prime number that is equal to , where n is an integer.For example, 31 is a Mersenne prime since . Write a computer program that finds all the Mersenne primes between 1 and
21. Sexy primes are two prime numbers that the difference between them is 6. For example, 23 and 29 are sexy primes since . Write a computer program that finds all the sexy primes between 1 and 300.
20. A safe prime is a prime number that can be written in the form where p is also a prime number. For example, 47 is a safe prime since and 23 is also a prime number. Write a computer program that
19. Write a MATLAB program in a script file that finds and displays all the numbers between 100 and 999 whose product of digits is 6 times the sum of the digits. [e.g. 347 since ]. Use a for-end loop
18. The Pythagorean theorem states that . Write a MATLAB program in a script file that finds all the combinations of triplesa, b, and c that are positive integers all smaller or equal to 50 that
17. A vector is given by x = [9 –1.5 13.4 13.3 –2.1 4.6 1.1 5 –6.1 10 0.2].Using conditional statements and loops, write a program that rearranges the elements of x in order from the smallest
16. Write a program that (a) generates a vector with 20 random integer elements with integers between 10 and 30, (b) replaces all the elements that are not even integers with random integers between
15. The value of can be estimated from the expression:Write a MATLAB program in a script file that determine for any number of terms. The program asks the user to enter the number of terms, and then
14. The value of can be estimated from:Write a program (using a loop) that determines for a given n. Run the program with n = 10, n = 100, and n = 1,000. Compare the result with pi. (Use format long.)
13. The reciprocal Fibonacci constant is defined by the infinite sum:where are the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, ... . Each element in this sequence of numbers is the sum of the previous
12. Fibonacci numbers are the numbers in a sequence in which the first three elements are 0, 1, and 1, and the value of each subsequent element is the sum of the previous three elements:0, 1, 1, 2,
11. The Pascal triangle can be displayed as elements in a lower-triangular matrix as shown on the right. Write a MATLAB program that creates a matrix that displays n rows of Pascal’s triangle. Use
10. The daily high temperature (°F) in New York City and Denver, Colorado, during the month of January 2014 is given in the vectors below (data from the U.S. National Oceanic and Atmospheric

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